EECE251
Circuit Analysis I
Lecture Integrated Program
Set 4: Operational Amplifiers
Shahriar Mirabbasi
Department of Electrical and Computer Engineering
University of British Columbia
shahriar@ece.ubc.ca
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EECE 251, Set 4
Amplifiers
•
There are various types of amplifiers.
•
Perhaps the most common type is a voltage amplifier (usually
referred to simply as an amplfier!) where both input and output
of the amplifier are voltages:
Vin
•
Vout
A bit more realistic schematic:
Vin
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Supply
+
+
-
-
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Vout
Common Ground
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Amplifiers
•
Typically, amplifiers have two supplies: One is positive (+Vcc)
and one is negative (–Vcc).
+Vcc
+
Vin
+
–Vcc
-
Vout
-
Common Reference (Ground)
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Saturation
•
A practical limitation for amplifiers (at least the ones that we will
see in this course) is that the magnitude of their output voltage
cannot exceed the supply, that is:
–Vcc ≤ Vout ≤ +Vcc
•
If the output wants to go beyond the supplies (for example when
the input is positive and large) then it will be clipped at +Vcc :
Vout = +Vcc
•
If the output is so negative then it will be limited by –Vcc:
Vout = –Vcc
•
In these cases we say that the amplifier is saturated
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Saturation
+Vcc
+
+
Vin
+Vcc
Vout
–Vcc
-
-
–Vcc
Common Reference (Ground)
•
Often for simplifying the drawings, the supplies and ground
connections of the amplifiers will not be explicitly shown
+Vcc
Vin
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+
+
-
-
Vout
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–Vcc
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Equivalent Model of a (Voltage) Amplifier
•
A voltage amplifier can be modeled with voltage-controlled
voltage source:
Vout = AVin
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Ideal Amplifier
•
What do you think the input and output resistance of an ideal
amplifier should be?
•
Let’s look at a example:
•
Let’s assume you have a signal source with a 50Ω resistance
(its Thevenin equivalent is the signal voltage source in series
with a 50Ω) and a load of 4Ω.
•
What happens if we naively connect the output of the signal
source to the load?
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Ideal Amplifier
•
What if we insert an amplifier between the source and the load.
•
In order to maximize the signal at the output can you guess what
should be the values for Rin and Rout?
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Ideal Amplifier
Rin → ∞ and Rout → 0
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Buffer
•
An amplifier with the gain of one is typically referred to as
“buffer”.
•
Buffers are very useful when one wants to “drive” a low
resistance with a signal source that has a large series
resistance.
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Differential Amplifier
•
An amplifier that has two inputs and amplifies the potential
difference between its input nodes (that is, it amplifies the
difference between the voltages of its two inputs)
inverting input
–
+
+
V2
+
non-inverting input
-
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+
Vout=A(V1-V2)
V1
-
-
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Equivalent Model for a Differential Amplifier
vd = v2 – v1 and vo = Avd = A(v2 –v1)
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Differential Amplifier
For ideal differential amplifier
Ri → ∞ and Ro → 0
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Operational Amplifier
•
Operational amplifier (or op amp for short) is a differential
amplifier whose gain is very large.
•
Ideal op amp is an ideal differential amplifier with infinite gain!
With Ri → ∞ and Ro → 0
and A → ∞
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Operational Amplifiers (Op Amps)
•
In light of their large gain, op amps are usually used in a
negative feedback configuration where their output is somehow
(usually through a passive component) is connected to their
negative (inverting) input.
•
If there is no feedback, what do you expect the output will be?
•
If Vp > Vn then the output will be saturated to the positive
supply. Why?
•
If Vp < Vn then the output will be saturated to the negative
supply
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Op Amp
•
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What is the relationship between Vp and Vn in an op amp with
negative feedback?
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Op Amp
•
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What is the relationship between Vp and Vn in an op amp with
negative feedback?
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Op Amps
•
Op amps were designed to performed mathematical operations
such as subtraction, addition, multiplication, division, integration,
and differentiation (therefore the name operational amplifier!).
•
So let’s have a look at how we can perform these operations
using op amps.
•
Note that in all these cases we should make sure that we have a
negative feedback. Why?
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Inverting Amplifier
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Example
•
What is the gain of this circuit, that is, what is vo/vi?
•
If vi=0.5V what is the output voltage? What is the current in the
10kΩ resistor?
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Non-inverting Amplifier
•
Find the gain (vo/vi) of the following circuit?
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Buffer
•
Also known as voltage follower or unity gain amplifier
•
What is the use of such amplifier?
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Example
•
In the following circuit, find the output voltage.
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Summing Amplifier
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Difference Amplifier
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Example
•
Design an op amp circuit with inputs v1 and v2 such that
vo= – 2v1+1.5v2
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Differentiator
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Integrator
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Logarithm!
•
Recall that for a diode we have
i
•
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D
≈
v
V
I
s
e
D
T
In the following circuit, find the relationship between vo and vi .
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Exponential
•
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In the following circuit, find the relationship between vo and vi .
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Multiplication and Division
•
Can you think of a circuit that can be used to multiply two
voltages?
•
How about a circuit that can be used to divide two voltages?
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Summary
•
Inverting amplifier
vo = −
•
R2
vi
R1
Non-inverting amplifier
 R 
vo = 1 + 2 vi
 R1 
•
Buffer (voltage follower)
vo = vi
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Summary
•
Summer (adder)
R
R
R

vo = − f v1 + f v2 + f v3 
R2
R3 
 R1
•
Difference Amplifier
vo =
R2
(v2 − v1 )
R1
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Summary
•
Differentiator
vo = − RC
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Integrator
vo = −
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dvi
dt
1
vi dt
RC ∫
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Summary
•
Taking natural logarithm
 v 
vo = −VT ln i 
 R ⋅ Is 
•
Raising to the power of e
vo = − R ⋅ I s e
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vi
VT
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Instrumentation Amplifier
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